ANALYTICAL FORMULAS OF SOLUTIONS OF GEOMETRICALLY NONLINEAR EQUATIONS OF AXISYMMETRIC PLATES AND SHALLOW SHELLS

Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equa- tions.

Analytical formulas for carrier density and Fermi energy in semiconductors with a tight-binding band

Analytical formulas for evaluating the relation of carrier density and Fermi energy for semiconductors with a tight-binding band have been proposed. The series expansions for a carrier density with fast convergency have been obtained by means of a Bessel function. A simple and analytical formula for Fermi energy has been derived with the help of the Gauss integration method. The results of the proposed formulas are in good agreement with accurate numerical solutions. The formulas have been successfully used in the calculation of carrier density and Fermi energy in a miniband superlattice system. Their accuracy is in the order of 10-5.

Analytical study on water hammer pressure in pressurized conduits with a throttled surge chamber for slow closure

This paper presents an analytical investigation of water hammer in a hydraulic pressurized pipe system with a throttled surge chamber located at the junction between a tunnel and a penstock, and a valve positioned at the downstream end of the penstock. Analytical formulas of maximum water hammer pressures at the downstream end of the tunnel and the valve were derived for a system subjected to linear and slow valve closure. The analytical results were then compared with numerical ones obtained using the method of characteristics. There is agreement between them. The formulas can be applied to estimating water hammer pressure at the valve and transmission of water hammer pressure through the surge chamber at the junction for a hydraulic pipe system with a surge chamber.

An analytic formula describing the plasma arc pressure distribution

In plasma arc welding process, the arc force plays a critical role in keyhole formation and weld pool behaviors. The widely used Gaussian mode of the arc pressure just considers the welding current, and other important factors are not involved. Thus, it needs to establish a new formula including the main process parameters. Based on the accelerated plasma impacting theory, a new analytic formula is derived to calculate the plasma arc pressure. It correlates the plasma arc pressure with the main process parameters such as the welding current, arc voltage, plasma gas flow rate, and nozzle size. The detail of the arc pressure derivation is given out. The measured and calculated data of the arc pressure are compared to validate the formula.

Strain analysis of buried steel pipelines across strike-slip faults

Existing analytical methods of buried steel pipelines subjected to active strike-slip faults depended on a number of simplifications.To study the failure mechanism more accurately,a refined strain analytical methodology was proposed,taking the nonlinear characteristics of soil-pipeline interaction and pipe steel into account.Based on the elastic-beam and beam-on-elastic-foundation theories,the position of pipe potential destruction and the strain and deformation distributions along the pipeline were derived.Compared with existing analytical methods and three-dimensional nonlinear finite element analysis,the maximum axial total strains of pipe from the analytical methodology presented are in good agreement with the finite element results at small and intermediate fault movements and become gradually more conservative at large fault displacements.The position of pipe potential failure and the deformation distribution along the pipeline are fairly consistent with the finite element results.

P-branch emission spectra of the A^1π-X^1Σ^+ system of IrN

The P-branch emission spectra of （4,1） and （3,1） bands of the A^1П-X^1∑^＋ system of IrN molecule are studied using an analytical formula which is derived from elementary expression of molecular total energy by taking multiple spectral differences. It not only reproduces the known experimental transition lines, but also predicts the unknown spectral lines up to J = 80 for each band by using a group of fifteen known experimental transition lines.

Gravity effect calculation of threedimensional linear density distribution andits application

An algorithm for calculating gravity effect of three-dimensional (3D) linear density distribution is presented in this paper. The linear continuous density distribution is represented with 3D grid model, which has a resemblance to the velocity model used in some seismic tomography codes. The consensus in representation method of density model and velocity model facilitates the seismic-gravity-integrated interpretation or simultaneous inversion. The numerical test of synthetic data shows that although the analytical gravity formula for linear density distribution is more complex than that for piecewise constant density distribution, it takes less time to calculate the gravity effect with linear density model than that with piecewise constant density model. In addition, this method is used in the integrated interpretation of 3D seismological tomography and gravity data in Dabie Mountain area.

Experimental and analytical studies on the deformability of a precast RC shear wall involving bolted connections

To study the deformability and ductility of an innovative precast shear wall joined by bolted connections,experimental tests were conducted on two test walls under monotonic and cyclic loading,respectively;subsequently,theoretical analysis was performed on the deformation performance of the shear wall assembly.The test results confirmed the favorable deformability and ductility of the specimens.The top displacement of the shear wall assembly was analytically decomposed into several constituent parts,the theoretical formulae of which were subsequently deduced.The compositional analysis demonstrated that the top displacement of the test wall was primarily induced by the elastic deformation of the upper wall panel(UWP),the relative slippages within the bolted connections,and the flexural deformation within the plastic region of the UWP,while the constituent part contributed by the deformation in the connecting steel frame can be neglected.

Modeling and analytical calculation of road damage coefficient considering tire pressure and damping of vehicles

The road damage coefficientβis a significant indicator to estimate the degree of the road damage caused by vehicles.The existing calculation method ofβis not convenient for the engineering application.To effectively evaluate the damage degree and facilitate the engineering application,this paper studied the simple and reliable analytical calculation method ofβ.Firstly,a dynamic model of the vehicle–road system was created.The tire pressure and the tire damping were considered in the model.Moreover,the relationship between the tire vertical stiffness and the tire pressure is approximated as a linear function.Secondly,based on the dynamic model,according to the definition ofβ,a concise analytical formula ofβwas derived and verified by numerical simulations.The relative errors of the analytical calculation results are all less than 0.1%.Thirdly,the influences of the tire pressure p,the damping ratioξs of the suspension system,and the damping ratioξt of the wheel system onβwere analyzed.Moreover,based on the analytical formula ofβ,a mathematical model of the optimal damping matching for the suspension system was established and a case study was also given.The research results show that the larger the tire pressure p,the larger the value ofβis.For each p,there is an optimal damping ratioξs.If the tire damping is ignored,it will lead to the design error forξs.Finally,some important conclusions were drawn.The analytical formula ofβand the conclusions can provide valuable references for the analysis of the road damage and the initial design of vehicle suspensions.

Analytical formula of rectangular surface mobility of an infinite plate and the parameters influences

This paper investigates the characteristics of surface mobility when power transmission over the contact area between sub-structures is considered. An analytical formula of the surface mobility of an infinite homogeneous plate over a rectangular contact area subject to a uniform, conphase force excitation is derived by using complex power method and the concept of structural intensity. This formula provides a theoretical tool for investigating power transmission over the contact area between sub-structures. The influences of the size, the dimension and the aspect ratio of the contact area on power transmission are analyzed and described according to the results calculated, that provides an effectively theoretical method for investigation of vibration isolation.

Analytical-BEM coupling method for fast 3-D interconnect resistance extraction

Deep submicron process technology is widely being used and interconnect structures are becoming more and more complex.This means that the resistance calculation based on two-dimensional models can no longer provide sufficiently accurate results.This paper presents a three-dimensional resistance calculation method called the combined analytical formula and boundary element method(ABEM).The method cuts selected interconnecting lines then it calculates the resistances of straight sections using an analytical formula and the resistances of the other sections using the boundary element method(BEM).The resistances of the different sub-regions are combined to calculate the resistance of the entire region.Experiments on actual layouts show that compared with the commercial software Raphael based on finite difference method,the proposed method is 2-3 orders of magnitude faster.The ABEM method uses much less memory(about 0.1%-1%),and is more accurate than Raphael with default mesh partitions.The results illustrate that the proposed method is efficient and accurate.

Analytical delay models for RLC interconnects under ramp input

Analytical delay models for Resistance Inductance Capacitance(RLC)interconnects with ramp input are presented for different situations,which include overdamped,underdamped and critical response cases.The errors of delay estimation using the analytical models proposed in this paper are less by 3%in comparison to the SPICE-computed delay.These models are meaningful for the delay analysis of actual circuits in which the input signal is ramp but not ideal step input.

Analytic models for organic field-effect transistors based on exponential and power mobility models

The fundamental I-V formula of an organic field effect transistor(OFET)is improved to overcome the divergence of the integrand,so it is very convenient for both numerical calculations and analytic derivations.The analytic I-V formulae are derived based on the exponential mobility model and power-function mobility model,respectively,and the derived analytic formulae are applied to three OFET devices.The results calculated from the reformulated analytic I-V formulae taking in exponential and power function mobility models are all in good agreement with the experimental I-V data.The parameters μ_(0) and γ that are extracted from the mobility model and fitted by experimental data show simple Arrhenius temperature dependence and inverse linear relationship with temperature,respectively.These findings are very useful for practical applications and device simulations.

Two-proton radioactivity of ground and excited states within a unified fission model

A unified fission model is extended to study two-proton radioactivity of the ground states of nuclei,and a good agreement between the experimental and calculated half-lives is found.The two-proton radioactivity half-lives of the ground states of some probable candidates are predicted within this model by inputting the released energies taken from the AME2020 table.It is shown that the predictive accuracy of the half-lives is comparable to those of other models.Then,two-proton radioactivity of the excited states of^(14)O,^(17,18)Ne,^(22)Mg,^(29)S,and^(94)Ag is discussed within the unified fission model and two analytical formulas.It is found that the experimental half-lives of the excited states are reproduced better within the unified fission model.Furthermore,the two formulas are not suitable for the study of two-proton radioactivity of excited states because their physical appearance deviates from the mechanism of quantum tunneling,and the parameters involved are obtained without including experimental data from the excited states.

New microscopic wave function of α-condensation

We explain how to treat a microscopic wave function of α-condensation taking a 3α-nucleus as a typical example. The wave function has been originally proposed ten years before by Horiuehi, Ropke, Schuck and the present author （Phys. Rev. Lett., 2001, 87： 192501）. The microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons, effective inter- nucleon forces and the Coulomb force, can play an important role in reproducing an α-gas nature thanks to α-condensation as an excited state of α-like nuclei. An essential point of the wave function is to describe their ground state simultaneously. We study its typical features by giving an analytical formula of the norm kernel and the kernel concerning the one-body operator for 3α-condensation.

Systematic description of nuclear electric quadrupole moments

The nuclear electric quadrupole moment （NQM） is one of the fundamental bulk properties of the nucleus with which nuclear deformations can be investigated. The number of measured NQMs is significantly less than that of known masses, and there is still no global NQM formula for all bound nuclei. In this paper, we propose an analytical formula, which includes the shell corrections and which is the function of the charge number, mass number, spin, charge radius, and nuclear deformation, for calculating the NQMs of all bound nuclei. Our calculated NQMs of 524 nuclei in their ground states are reasonable compared to the experimental data based on the nuclear deformation parameters derived from the Weizsacker-Skyrme （WS） nuclear mass models. Smaller rms deviations between the calculated NQMs and experimental data indicate that the deformation parameters predicted from the WS mass models are reasonable. In addition, 161 unmeasured NQMs with known spins are also predicted with the proposed formula.